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In this paper, we propose a variable selection method for generalnonparametric kernel-based estimation. The proposed method consists oftwo-stage estimation: (1) construct a consistent estimator of the targetfunction, (2) approximate the estimator using a few variables by l1-typepenalized estimation. We see that the proposed method can be applied to variouskernel nonparametric estimation such as kernel ridge regression, kernel-baseddensity and density-ratio estimation. We prove that the proposed method has theproperty of the variable selection consistency when the power series kernel isused. This result is regarded as an extension of the variable selectionconsistency for the non-negative garrote to the kernel-based estimators.Several experiments including simulation studies and real data applicationsshow the effectiveness of the proposed method.

Variable Selection for Nonparametric Learning with Power Series Kernels